Hands-on Exercise 2

pacman::p_load(sf, terra, spatstat, tmap, rvest, tidyverse)

Read Polygon Layer

mpsz_sf <- st_read("data/MasterPlan2019SubzoneBoundaryNoSeaKML.kml") |>
  st_zm(drop = TRUE, what = "ZM") |>
  st_transform(crs = 3414)

Reading layer `URA_MP19_SUBZONE_NO_SEA_PL' from data source 
  `D:\edithting\ISSS626v1\Hands-on_Ex\Hands-on_Ex02\data\MasterPlan2019SubzoneBoundaryNoSeaKML.kml' 
  using driver `KML'
Simple feature collection with 332 features and 2 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 103.6057 ymin: 1.158699 xmax: 104.0885 ymax: 1.470775
Geodetic CRS:  WGS 84

extract_kml_field <- function(html_text, field_name) {
  if (is.na(html_text) || html_text == "") return(NA_character_)
  page <- rvest::read_html(html_text)
  rows <- page |> html_elements("tr")
  value <- rows |>
    keep(~ html_text2(html_element(.x, "th")) == field_name) |>
    html_element("td") |>
    html_text2()
  if (length(value) == 0) NA_character_ else value
}

mpsz_sf <- mpsz_sf |>
  mutate(
    REGION_N = map_chr(Description, extract_kml_field, "REGION_N"),
    PLN_AREA_N = map_chr(Description, extract_kml_field, "PLN_AREA_N"),
    SUBZONE_N = map_chr(Description, extract_kml_field, "SUBZONE_N"),
    SUBZONE_C = map_chr(Description, extract_kml_field, "SUBZONE_C")
  ) |>
  select(-Name, -Description) |>
  relocate(geometry, .after = last_col())

mpsz_cl <- mpsz_sf |>
  filter(SUBZONE_N != "SOUTHERN GROUP",
         PLN_AREA_N != "WESTERN ISLANDS",
         PLN_AREA_N != "NORTH-EASTERN ISLANDS")

Read Point Layer

childcare_sf <- st_read("data/ChildCareServices.kml") |>
  st_zm(drop = TRUE, what = "ZM") |>
  st_transform(crs = 3414)

Reading layer `CHILDCARE' from data source 
  `D:\edithting\ISSS626v1\Hands-on_Ex\Hands-on_Ex02\data\ChildCareServices.kml' 
  using driver `KML'
Simple feature collection with 1925 features and 2 fields
Geometry type: POINT
Dimension:     XYZ
Bounding box:  xmin: 103.6878 ymin: 1.247759 xmax: 103.9897 ymax: 1.462134
z_range:       zmin: 0 zmax: 0
Geodetic CRS:  WGS 84

tmap_mode("view")

ℹ tmap mode set to "view".

tm_shape(childcare_sf) + tm_dots()

Registered S3 method overwritten by 'jsonify':
  method     from    
  print.json jsonlite

tmap_mode("plot")

ℹ tmap mode set to "plot".

Convert to spatstat objects

childcare_ppp <- spatstat.geom::as.ppp(childcare_sf)
sg_owin       <- spatstat.geom::as.owin(mpsz_cl)
childcareSG_ppp <- childcare_ppp[sg_owin]

Clark-Evans Tests

# Z-test
spatstat.explore::clarkevans.test(
  childcareSG_ppp,
  correction = "none",
  clipregion = "sg_owin",
  alternative = "clustered"
)

    Clark-Evans test
    No edge correction
    Z-test

data:  childcareSG_ppp
R = 0.53532, p-value < 2.2e-16
alternative hypothesis: clustered (R < 1)

# Monte Carlo test
spatstat.explore::clarkevans.test(
  childcareSG_ppp,
  correction = "none",
  clipregion = "sg_owin",
  alternative = "clustered",
  method = "MonteCarlo",
  nsim = 99
)

    Clark-Evans test
    No edge correction
    Monte Carlo test based on 99 simulations of CSR with fixed n

data:  childcareSG_ppp
R = 0.53532, p-value = 0.01
alternative hypothesis: clustered (R < 1)

KDE

library(spatstat.explore)
library(spatstat.model)
library(spatstat.geom)

bw <- bw.diggle(childcareSG_ppp)

kde_childcareSG <- density.ppp(childcareSG_ppp, sigma = bw)

plot(kde_childcareSG)

Rasterize KDE and map

kde_rast <- terra::rast(kde_childcareSG)
terra::crs(kde_rast) <- "EPSG:3414"

tmap_mode("plot")

ℹ tmap mode set to "plot".

tm_shape(kde_rast) +
  tm_raster(col.scale = tm_scale_continuous(values = "viridis"),
            col.legend = tm_legend(title = "Density (per km²)",
                                   title.size = 0.7, text.size = 0.7,
                                   bg.color = "white", bg.alpha = 0.7,
                                   position = tm_pos_in("right","bottom"),
                                   frame = TRUE)) +
  tm_graticules(labels.size = 0.7) +
  tm_compass() +
  tm_layout(scale = 1)

[plot mode] legend/component: Some components or legends are too "high" and are
therefore rescaled.
ℹ Set the tmap option `component.autoscale = FALSE` to disable rescaling.

By Planning Area

library(spatstat.explore)
library(spatstat.model)
library(spatstat.geom)   # or install from GitHub
library(spatstat.explore)

# Filter by planning area
pg <- mpsz_cl |> filter(PLN_AREA_N == "PUNGGOL")
tm <- mpsz_cl |> filter(PLN_AREA_N == "TAMPINES")
ck <- mpsz_cl |> filter(PLN_AREA_N == "CHOA CHU KANG")
jw <- mpsz_cl |> filter(PLN_AREA_N == "JURONG WEST")

# Convert to ppp objects
pg_ppp <- childcare_ppp[as.owin(pg)]
tm_ppp <- childcare_ppp[as.owin(tm)]
ck_ppp <- childcare_ppp[as.owin(ck)]
jw_ppp <- childcare_ppp[as.owin(jw)]

# Rescale to km
pg_km <- rescale(pg_ppp, 1000, "km")
tm_km <- rescale(tm_ppp, 1000, "km")
ck_km <- rescale(ck_ppp, 1000, "km")
jw_km <- rescale(jw_ppp, 1000, "km")

# Clark–Evans test in Tampines
clarkevans.test(tm_ppp, correction="none", alternative="two.sided", nsim=999)

    Clark-Evans test
    No edge correction
    Z-test

data:  tm_ppp
R = 0.66817, p-value = 6.58e-12
alternative hypothesis: two-sided

# KDE in Punggol
bw_pg <- bw.diggle(pg_km)
kde_pg <- density.ppp(pg_km, sigma = bw_pg, edge = TRUE, kernel = "gaussian")
plot(kde_pg, main = "Punggol KDE")

Chapter 05

Importing spatial data

library(sf)
library(tmap)
library(spatstat)

library(dplyr)

# Childcare centres (point data)
childcare_sf <- st_read("data/ChildCareServices.kml")

Reading layer `CHILDCARE' from data source 
  `D:\edithting\ISSS626v1\Hands-on_Ex\Hands-on_Ex02\data\ChildCareServices.kml' 
  using driver `KML'
Simple feature collection with 1925 features and 2 fields
Geometry type: POINT
Dimension:     XYZ
Bounding box:  xmin: 103.6878 ymin: 1.247759 xmax: 103.9897 ymax: 1.462134
z_range:       zmin: 0 zmax: 0
Geodetic CRS:  WGS 84

# URA Master Plan 2019 Subzone Boundary (No Sea) (polygon data)
mpsz_sf <- st_read("data/MasterPlan2019SubzoneBoundaryNoSeaKML.kml")

Reading layer `URA_MP19_SUBZONE_NO_SEA_PL' from data source 
  `D:\edithting\ISSS626v1\Hands-on_Ex\Hands-on_Ex02\data\MasterPlan2019SubzoneBoundaryNoSeaKML.kml' 
  using driver `KML'
Simple feature collection with 332 features and 2 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 103.6057 ymin: 1.158699 xmax: 104.0885 ymax: 1.470775
Geodetic CRS:  WGS 84

summary(childcare_sf)

     Name           Description                 geometry   
 Length:1925        Length:1925        POINT Z      :1925  
 Class :character   Class :character   epsg:4326    :   0  
 Mode  :character   Mode  :character   +proj=long...:   0  

summary(mpsz_sf)

     Name           Description                 geometry  
 Length:332         Length:332         MULTIPOLYGON :332  
 Class :character   Class :character   epsg:4326    :  0  
 Mode  :character   Mode  :character   +proj=long...:  0  

Visualizing Data Layers

tmap_mode('view')

ℹ tmap mode set to "view".

tm_shape(childcare_sf) + tm_dots()

tmap_mode('plot')

ℹ tmap mode set to "plot".

Handling Duplicate Points

any(duplicated(childcare_ppp))

[1] FALSE

multiplicity(childcare_ppp)

   [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
  [38] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
  [75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [112] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [149] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [186] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [223] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [260] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [297] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [334] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [371] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [408] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [445] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [482] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [519] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [556] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [593] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [630] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [667] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [704] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [741] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [778] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [815] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [852] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [889] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [926] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [963] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1000] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1037] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1074] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1111] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1148] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1185] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1222] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1259] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1296] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1333] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1370] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1407] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1444] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1481] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1518] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1555] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1592] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1629] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1666] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1703] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1740] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1777] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1814] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1851] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1888] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1925] 1

sum(multiplicity(childcare_ppp) > 1)

[1] 0

childcare_ppp_jit <- rjitter(childcare_ppp, retry = TRUE, nsim = 1, drop = TRUE)
any(duplicated(childcare_ppp_jit))

[1] FALSE

G-Function

Choa Chu Kang

G_CK <- Gest(ck_km, correction = "border")
plot(G_CK)

G_CK.csr <- envelope(ck_km, Gest, nsim = 999)

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

plot(G_CK.csr)

Tampines

G_tm <- Gest(tm_km, correction = "best")
plot(G_tm)

G_tm.csr <- envelope(tm_km, Gest, correction = "all", nsim = 999)

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

plot(G_tm.csr)

F-Function

Choa Chu Kang

F_CK <- Fest(ck_km)
plot(F_CK)

F_CK.csr <- envelope(ck_km, Fest, nsim = 999)

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

plot(F_CK.csr)

Tampines

F_tm <- Fest(tm_km, correction = "best")
plot(F_tm)

F_tm.csr <- envelope(tm_km, Fest, correction = "all", nsim = 999)

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

plot(F_tm.csr)

K-Function

Choa Chu Kang

K_ck <- Kest(ck_km, correction = "Ripley")
plot(K_ck, . - r ~ r)

K_ck.csr <- envelope(ck_km, Kest, nsim = 99, rank = 1, glocal = TRUE)

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

plot(K_ck.csr, . - r ~ r)

Tampines

K_tm <- Kest(tm_km, correction = "Ripley")
plot(K_tm, . - r ~ r, xlim = c(0,1000))

K_tm.csr <- envelope(tm_km, Kest, nsim = 99, rank = 1, glocal = TRUE)

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

plot(K_tm.csr, . - r ~ r, xlim = c(0,500))

Error in UseMethod("distmap") : 
  no applicable method for 'distmap' applied to an object of class "im"

L-Function

Choa Chu Kang

L_ck <- Lest(ck_km, correction = "Ripley")
plot(L_ck, . - r ~ r)

L_ck.csr <- envelope(ck_km, Lest, nsim = 99, rank = 1, glocal = TRUE)

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

plot(L_ck.csr, . - r ~ r)

Tampines

L_tm <- Lest(tm_km, correction = "Ripley")
plot(L_tm, . - r ~ r, xlim = c(0,1000))

L_tm.csr <- envelope(tm_km, Lest, nsim = 99, rank = 1, glocal = TRUE)

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

plot(L_tm.csr, . - r ~ r, xlim = c(0,500))

Error in UseMethod("distmap") : 
  no applicable method for 'distmap' applied to an object of class "im"